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Stochastic Heat Equations with Values in a Riemannian Manifold (1706.05979v1)
Published 19 Jun 2017 in math.PR, math.AP, math.DG, and math.FA
Abstract: The main result of this note is the existence of martingale solutions to the stochastic heat equation (SHE) in a Riemannian manifold by using suitable Dirichlet forms on the corresponding path/loop space. Moreover, we present some characterizations of the lower bound of the Ricci curvature by functional inequalities of various associated Dirichlet forms.